Mourinho acted through lawyers against sports daily Marca's editor-in-chief Roberto Palomar following an article he wrote that was published on Monday.
"Palomar ... referred to our client as 'the type of person who would flee after knocking someone down'," said an extract of a letter from Mourinho's lawyers published in Thursday's Marca.
"In our eyes this phrase is ... degrading and was used in a manner which was completely unnecessary in the critique."
The newspaper said that Mourinho has demanded the article be rectified and 15,000 euros ($19,600) in damages which he will donate to the local football team his son plays for.
In a separate statement on the club website, Real said they had instructed their legal department to take the action they considered appropriate against Alfons Godall, a Barca director during Joan Laporta's presidency of the Catalan club.
After Mourinho slid on to the Bernabeu pitch on his knees celebrating Cristiano Ronaldo's 90th-minute winner in their 3-2 Champions League victory over Manchester City on Tuesday, Godall took to his Twitter account.
"It's lamentable the psychopath celebrating goals as if he was a player," Godall wrote.
In their statement, the league champions said: "Real Madrid is not going to allow attacks of this kind and will always take action against those who question the honour of people who form a part of this club."
Although Godall is not a member of the current Barcelona board, these events will no doubt stir up the animosity between the great rivals again ahead of Real's visit to the Nou Camp in La Liga on October 7.